Duality in Mechanics

Given an electric network E• which has M meshes and P node-pairs, its electric dual El will have P meshes and M node-pairs and its classical mechanical nalog M! will have M+ 1 nodes, M independent ode-pairs, and P independent node cycles. A second mechanical system M•, the classical analog of El, will have M cycles and P node-pairs. If, for example, M= 2, P= 3, the systems E• and M•, analogs in the Firestone or "mobility" method, will be governed by two mesh equations, expressing that the algebraic sum of the voltages or velocities around any loop is zero; the systems Ei and Mj-• also Firestone analogs, will satisfy two node equations, expressing that the algebraic sum of the currents or forces leaving any node is zero. These four sets of equations are identical, interchanging symbols uitably. The consideration of the four systems, Ev, E6 My, Mf, forming a complete set, shows the advantages of the Firestone over the classical system of analogies and suggests a systematic use of duality in mechanical s well as in electrical systems.